Can someone solve these equations:?

Question

1)

x+4= 4/x+4 +2



2)

5/x+2= x/3

3)

x^2/x^2-4=x/x+2=2x/2-x

Answer 1

It helps, when you have to write an equation on a line, to use parentheses so that it is clear what is included in the denominator. I hope I've assumed correctly.

x + 4 = 4/(x + 4) + 2
x + 4 - 2 = 4/(x + 4)
(x + 2)(x + 4) = 4
x^2 + 6x + 8 = 4
x^2 + 6x + 4 = 0
x = (-6 +/- sqrt(36 - 16))/2
x = (-6 +/- sqrt(20))/2
x = (-6 +/- 2 * sqrt(5))/2
x = -3 +/- sqrt(5)


5/(x + 2) = x/3
5 = x * (x + 2)/3
15 = x * (x + 2)
15 = x^2 + 2x
x^ + 2x - 15 = 0
x = 5 or -3 (This one is easy)


I don't understand the last equation. There's too many equals signs.

Answer 2

I'll solve one and only one:

x+4= 4/x+4 +2
(x+4)(x+4) = 4 + 2(x+4)
x² + 8x + 16 = 4 + 2x + 8
x² + 6x + 4 = 0

Use the quadratic:

[-b +- √b² - (4)(a)(c)] 2a

=

-6 +- √36 - 16
-6 +- √20
(-6 +- 2√5)/2 is your answer.